+195 In the figure, AD = CD and AB = CB .
(i) Prove that Line BD bisects angle ADC (i.e. that line BD cuts angle ADC into two equal angles).
(ii) Prove that Line AC and Line DB are perpendicular.
+129849 Since AD = CD
Then the angles opposite these sides are also equal
So angle DAC = angle DCA
And if AB = CB, then the angles opposite thes sides are also equal
So angle CAB = angle ACB
So angle DAC + angle CAB = angle DCA + angle ACB
So angle DAB = angle CDB
Then, by SAS....triangle DAB = triangle DCB
Then angle ADB = angle CDB.....so angle ADC is bisected
And angle DAC = angle DCA
AD = CD
And angle DAC = angle DCA
So....by ASA....triangle EAD = triangle ECD
So angle AED = angle CED
And, by Euclid.....a line standing upon a line that makes adjacent angles equal means that the lines are perpendicular....so AC and Db are perpendicular
